Map



- oct. 13,1925.

K. G. KARSTEN y MAP *Filed April 5, 1923 11\1vENToR Karl Gizfrrswven,

tion,

area, indifferent States, counties Patented Oct. 13, 1925.

naar. e. xAns'rnN, or New YORK, N. Y.

MAP;

Application. ined. Aprils,

To allwlwm t may concern: -Be it known that` 1 KARL G. KARs'rEN, a citizen of. thev United. States, and resident of Newv York, in the county of New York and State of. New York, have invented certain new. and useful: :Improvements in Maps, of which the following is a specification. ,f

' This v invention. relates to maps for graphically displaying the relative importance of various geographical unitslupon the basis of population, or any factor other than total lanzdarea', of such units, the map. being formed. by distorting boundaries to make the included; map surface correspond in area with the Value of. such unit upon. such basis Vwithout` losingfamiliar and significant features of the unit outline.

' An important object ofthe invention is to provide a means to facilitateY the study of comparative values of. diderent States,

" counties, or other. geographical or' political.

units or divisions, with regard ltol populawealth, natural resources, or: any other factor" Ather than. total: land: area, ther pres'- ent basis of inap projection.I

l Another. object of. theinvention isy to provide a means' tol facilitate the study of distribution orI location of distributing points, branch houses, supply stations, or other points', withA reference. to population, wealth, resources, or other factors except total land orY other geographical orf political units..

The map embodying my invention is made by drawing the various States, counties' or 'geographical orpolitical units or divisions out of true proportion, on such projection as will increase totalland area by the actual density coefficient of value with respect to population, Wealth', resources, or any other factor.' except total land. area, thus making the mapi surface of such units correspond in areaiwith the total value of such unit asregards population-- wealth, or' otherY factor except total land value, such projection beso' applied; as to preserve and retain familiar, significant, and recognizable' features: of the boundaries or outlines of such units, sufficiently to make the units recognizable and approximately characteristic, while distorting them suflicientlyY tor make their size or map surface accurately correarea with valueasaforesaid. Thus while outlines upon suchiamafp` are dist-orted',- the. .'areinot distorted Vmorefth'anis necessary' or theI accurate` representation of 192s, serial No. 629,569.

value. And suchl a map thereforel differs from accustomed maps inuthat. while the latter is drawn to represent square miles or other measurement of total land. area',y such aina-pl 1s drawn to represent and correspond with` the actual value of any factor other than total land area. f

There are several methods of. producing such al inap,A any and all of which are covered by the appended claims with: respect topurpose and function.: For preciseI puriposes the drafting instrument known as' the p-lan-imeter will verify the map area after tentative drawing.. For rough 'purposes erosseruledi paper inl which each square' on the paper is taken to represent a certain quantityi-n thev value of the factor used. for representation, will. be sufficient-ly accurate, andthe map surface may be: measured; by

counting. squares and parts of squares so'- measured. or weighed, with the value of the.

factor, the clay or other' substance of different colors'being used'y for different units or divisions, and modeled' into'- the familiar outlines and. flattened to uniformv thickness, and a copy of the whole, when completed, being made.l byy photograph or tracing-.paper orother means.y For study ofdistribution, rnap-pins, labels, tags, circles, dots, or other Ymarks may be' made upon theVy map embodying my invention, at points thereon. These nstancesof. drafting are cited to showl how a densitylprojection: map may be obtained, thefnrap itself, as a vprocess ini graphic presentation, andas a means to graphically display values, and tothe-study of values,.otlier than total. land area, and as a means to the study 1 of distribution in respectA to-y any factor,- other than total landar-ea, being the subjeot'offthispetition.`

En the drawing whih is intended as` a graphic representation of the States New York, New Jersey and'. Pennsylvania, the numeral .5f indicates the distorted boundary of New York and the numerals 6y and 7 in'- dicatev respectively the distorted 'boundaries ofPennsylvan-ia andNew Jersey. The map area included within` the-boundary lines 5, 6

and Toff-` therespect-ive States New York,

respective-`population ofl these States. 'It

vseveral territories.

will further be noted that the boundaries of these several States have been distorted without destroying the familiar and significant features of their true geographical outlines. In projecting the inap embodying my invention the actual land area of a given l territory is not taken into consideration as a factor. The only factor to be considered in distorting the boundaries of several given territories when projecting a map embodying my invention is that factor with which one is particularly concerned. For eX- ample: should the population be the selected factorthen the relative ultimate areas of the distorted territories is determined by the relative population of the several territories. Again should the value of the natural resources (as iron ore) be the selected factor then the relative ultimate areas of the distorted territories is determined by the relative value of the natural resources of the The uses to which the map embodying my invention may be put are innumerable. I therefore deem it necessary to elaborate on only one of these many uses. To make its application clear let us suppose that an industrial enterprise desires to distribute sales stations throughout the States of New York, Pennsylvania and New Jersey, in such a manner as to supply equal portions of the population from each of the several stations as indicated by the dots 8, 9 and 10 within the areas included respectively between the boundaries 5, 6 and 7 these areas representing respectively New York, Pennsylvania and New Jersey. By actual plotting since the given areas are represented according to their relative population the stations as indicated at 8, 9 and 10 may be evenly distributed throughout tliese given territories thus designating at a glance in which lo- -cality of a given territory each of the stations should be located.

In use, I desire to indicate by the area of circles the relative population of one city with respect to another. In the drawing I vhave shown circles l1 and l2, the areas of which represent respectively the population of New York city and Philadelphia. The population of New York city is approximately three times that of Philadelphia but by actually determining the ratio between the areas of the circles l1 and 12 the eXact ratio of population of New York city with respect to Philadelphia may be determined. The ratio between the population of New York city and Philadelphia having been determined the ratio between the number of sales stations of New York city and Philadelphia is readily fixed. It is to be noted that the boundaries of the territories are so distorted as to provide arcs of circles around the border cities these arcs of circles being completed diagrammatically as shown by thedotted lines of the figure to form circles, the areas of which circles as hereinbefore described is dependent upon the population of a given city with respect to a second given city.

It will be noted that I have shown only two cities, namely, New York and Philadelphia, as included in the circles liereinbefore referred to. I have selected these cities because of the fact that their population is in Vexcess of one million. It might be desired in some instances to include within the circles all of the cities having ay population in excess of five hundred thousand or for other purposes it might be desirable to include within circles vonly those cities havling a population of between say one hundred thousand and two hundred and fifty thousand.

It is to be understood that Vthe form of my invention herewith shown and described is to be taken as a preferred example of the same, and that various changes in the shape, size and arrangement of parts may be resorted to without departing fromV the spirit of the invention or the scope of the subjoined claims.

Having thus described my invention, what I claim as new and .desire to secure vand protect by Letters Patent of the United States, is:

l. A map of a plurality of territories having their boundary lines so distorted as to make their included areas graphically the relative importance of a given factor other than land area of one area with respect to another area, the boundaries being distorted withoutlosing their familiar and significant features certain cities of said territories indicated on said map by a geometric form having inscribed areas proportionate to the value of said factor pr-esent in said cities.

represent 'V 2. A map of a plurality of territories having their boundary lines so distorted as to make their included areas represent graphically the relative importance of a given factor other than land area of one area with respect to another area, `a portion of a boundary line in proximity to a border city being distorted `to form approXimately an arc of a circle and said city being included within the circle formed in y part of said arc.

3. A map of a plurality of territories having their boundary lines so4 distorted as to make their included areas represent graphically the relative importance of a given factor other than land area of one area with respect to another area, a portion of the boundary line in proximity to a border city of one of the territories being distorted to form part of the outline being included within the outlines of said vof a vregular figure, said boundary city figure, and said boundary line being distorted Withoutflosing 'its familiar and significant feat-ure.

4. A political map designed to represent approximately two known territories with their included areas representing graphically the relative importance of a given factor other than land area While maintaining somewhat their familiar appearance, and one of said territories having one of its cities indicated on said map by a form having an inscribed area proportionate to the value of said factor present in said city.

5. A map including a territory having an inscribed area representing graphically aV given factor other than land area of said territory and one of the cities of said territoryf. being represented thereon with a formfhaving an inscribed area proportionate to the value of said factor present in said city.

6. A map of a plurality of territories having their boundry lines distorted to maketheir included areas represent graphically Vthe population of the territories, While maintaining approximately the familiar outlines of the territories, certain cities in said territories being represented graphically by similarly shaped forms and having inscribed areas proportionate to the population of the several cities.

KARL G. KARSTEN. 

